MIP2601
Assignment 1
Unique NO: 601617
DUE: 13 MAY 2026
,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics
UNIVERSITY OF SOUTH AFRICA
Department of Mathematics Education
ASSIGNMENT 1
MIP2601 – Mathematics for Intermediate Phase Teachers III
UNDERSTANDING AND APPLYING THE VAN HIELE FRAMEWORK
IN INTERMEDIATE PHASE MATHEMATICS EDUCATION
Student Name: ___________________________
Student Number: ___________________________
Module: MIP2601
Unique Assignment No.: 601617
Due Date: 13 May 2026
Lecturer: Dr PD Motseki
University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 1
,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics
STUDENT DECLARATION
I, the undersigned, declare that:
1. I understand what plagiarism entails and am aware of the University's policy in
this regard.
2. This assignment is my own, original work. Where I used someone else's work,
whether a printed source, the internet or any other source, I give the proper
acknowledgement and include a complete reference list.
3. I did not use another current or previous student's work, submitting it as my
own.
4. I did not allow and will not allow anyone to copy my work with the intention of
submitting it as his or her own work.
Full Name: _______________________________________________
Student Number: _________________________________________
Signature: ______________________________________________
Date: ___________________________________________________
University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 2
,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics
Table of Contents
STUDENT DECLARATION ........................................................................................ 2
SECTION A: Conceptual Understanding of the Van Hiele Framework ...................... 5
A.1 Origin and Historical Background of the Van Hiele Theory .............................. 5
A.2 Key Ideas of the Van Hiele Theory ................................................................... 6
A.3 The Five Van Hiele Levels with Detailed Examples ......................................... 7
Level 0: Visualisation .......................................................................................... 7
Level 1: Analysis ................................................................................................. 8
Level 2: Informal Deduction ................................................................................ 8
Level 3: Formal Deduction .................................................................................. 8
Level 4: Rigor ...................................................................................................... 9
A.4 Visual Representation: The Van Hiele Levels as a Staircase ........................... 9
SECTION B: Diagnostic Task Analysis .................................................................... 11
B.1 Design of the Diagnostic Assessment ............................................................ 11
Full Diagnostic Tasks (As Given to Learners) ................................................... 12
B.2 Interpreting Learner Responses ..................................................................... 13
SECTION C: Lesson Design and Application ........................................................... 15
C.1 Lesson Plan 1 – Van Hiele Level 0: Visualisation (Grade 4) .......................... 15
Phase 1: Introduction / Motivation (10 minutes) ................................................ 15
Phase 2: Teaching Activity – Shape Hunt and Sort (25 minutes) ...................... 16
Phase 3: Class Discussion and Shape Gallery (15 minutes) ............................ 16
Phase 4: Assessment (10 minutes) ................................................................... 17
C.2 Lesson Plan 2 – Van Hiele Level 2: Informal Deduction (Grade 6) ................ 18
Phase 1: Review and Activation (10 minutes) ................................................... 18
Phase 2: The Quadrilateral Hierarchy Challenge (25 minutes) ......................... 18
Phase 3: Gallery Walk and Peer Assessment (15 minutes) .............................. 19
Phase 4: Assessment Task (10 minutes) .......................................................... 20
SECTION D: Curriculum Integration – Van Hiele Theory and CAPS ....................... 22
D.1 The CAPS Geometry Curriculum in the Intermediate Phase ......................... 22
D.2 CAPS Alignment with Van Hiele Levels ......................................................... 22
D.3 Scaffolding Geometry Teaching Using the Van Hiele Framework.................. 23
1. Level-Appropriate Language and Questioning .............................................. 23
2. Concrete–Representational–Abstract (CRA) Progression ............................ 24
3. Collaborative and Inquiry-Based Learning .................................................... 24
D.4 Identifying Missed Opportunities in Current Practice ...................................... 24
SECTION E: Reflective Commentary ....................................................................... 26
E.1 Reflecting on My Own Understanding of Geometry ....................................... 26
University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 3
, MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics
E.2 How the Van Hiele Framework Has Influenced My Teaching Approach ........ 26
E.3 Challenges and Areas for Further Growth ...................................................... 27
E.4 The Van Hiele Framework as a Lifelong Teaching Tool ................................. 28
REFERENCE LIST................................................................................................... 29
University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 4
Assignment 1
Unique NO: 601617
DUE: 13 MAY 2026
,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics
UNIVERSITY OF SOUTH AFRICA
Department of Mathematics Education
ASSIGNMENT 1
MIP2601 – Mathematics for Intermediate Phase Teachers III
UNDERSTANDING AND APPLYING THE VAN HIELE FRAMEWORK
IN INTERMEDIATE PHASE MATHEMATICS EDUCATION
Student Name: ___________________________
Student Number: ___________________________
Module: MIP2601
Unique Assignment No.: 601617
Due Date: 13 May 2026
Lecturer: Dr PD Motseki
University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 1
,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics
STUDENT DECLARATION
I, the undersigned, declare that:
1. I understand what plagiarism entails and am aware of the University's policy in
this regard.
2. This assignment is my own, original work. Where I used someone else's work,
whether a printed source, the internet or any other source, I give the proper
acknowledgement and include a complete reference list.
3. I did not use another current or previous student's work, submitting it as my
own.
4. I did not allow and will not allow anyone to copy my work with the intention of
submitting it as his or her own work.
Full Name: _______________________________________________
Student Number: _________________________________________
Signature: ______________________________________________
Date: ___________________________________________________
University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 2
,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics
Table of Contents
STUDENT DECLARATION ........................................................................................ 2
SECTION A: Conceptual Understanding of the Van Hiele Framework ...................... 5
A.1 Origin and Historical Background of the Van Hiele Theory .............................. 5
A.2 Key Ideas of the Van Hiele Theory ................................................................... 6
A.3 The Five Van Hiele Levels with Detailed Examples ......................................... 7
Level 0: Visualisation .......................................................................................... 7
Level 1: Analysis ................................................................................................. 8
Level 2: Informal Deduction ................................................................................ 8
Level 3: Formal Deduction .................................................................................. 8
Level 4: Rigor ...................................................................................................... 9
A.4 Visual Representation: The Van Hiele Levels as a Staircase ........................... 9
SECTION B: Diagnostic Task Analysis .................................................................... 11
B.1 Design of the Diagnostic Assessment ............................................................ 11
Full Diagnostic Tasks (As Given to Learners) ................................................... 12
B.2 Interpreting Learner Responses ..................................................................... 13
SECTION C: Lesson Design and Application ........................................................... 15
C.1 Lesson Plan 1 – Van Hiele Level 0: Visualisation (Grade 4) .......................... 15
Phase 1: Introduction / Motivation (10 minutes) ................................................ 15
Phase 2: Teaching Activity – Shape Hunt and Sort (25 minutes) ...................... 16
Phase 3: Class Discussion and Shape Gallery (15 minutes) ............................ 16
Phase 4: Assessment (10 minutes) ................................................................... 17
C.2 Lesson Plan 2 – Van Hiele Level 2: Informal Deduction (Grade 6) ................ 18
Phase 1: Review and Activation (10 minutes) ................................................... 18
Phase 2: The Quadrilateral Hierarchy Challenge (25 minutes) ......................... 18
Phase 3: Gallery Walk and Peer Assessment (15 minutes) .............................. 19
Phase 4: Assessment Task (10 minutes) .......................................................... 20
SECTION D: Curriculum Integration – Van Hiele Theory and CAPS ....................... 22
D.1 The CAPS Geometry Curriculum in the Intermediate Phase ......................... 22
D.2 CAPS Alignment with Van Hiele Levels ......................................................... 22
D.3 Scaffolding Geometry Teaching Using the Van Hiele Framework.................. 23
1. Level-Appropriate Language and Questioning .............................................. 23
2. Concrete–Representational–Abstract (CRA) Progression ............................ 24
3. Collaborative and Inquiry-Based Learning .................................................... 24
D.4 Identifying Missed Opportunities in Current Practice ...................................... 24
SECTION E: Reflective Commentary ....................................................................... 26
E.1 Reflecting on My Own Understanding of Geometry ....................................... 26
University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 3
, MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics
E.2 How the Van Hiele Framework Has Influenced My Teaching Approach ........ 26
E.3 Challenges and Areas for Further Growth ...................................................... 27
E.4 The Van Hiele Framework as a Lifelong Teaching Tool ................................. 28
REFERENCE LIST................................................................................................... 29
University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 4
